On the other one, within dark sector we can propose new ansatzes for both \(\bar{Q}\)  and \(\mathrm {\omega _{DE}}\) , which can be expanded in terms
of the Chebyshev polynomials \(T_{n}\) , defined in the interval \([-1,1]\)  and with a divergence-free \(\mathrm {\omega _{DE}}\)  at z\(\rightarrow -1\)  [1]}, [2]}.
However, that polynomial base was particularly chosen due to its rapid convergence and better stability than others, by giving minimal
errors [3]}, [4]}. Besides, \(\bar{Q}\)  could also be proportional to the DM energy density \(\mathrm {{\bar{\rho }}_{DM}}\) 
and to the Hubble parameter \(\bar{H}\) . This new model will guarantee an accelerated scaling attractor and connect to a standard
evolution of the matter. Here, \(\bar{Q}\)  will be res-tricted from the criteria exhibit in [5]}.
